A possible embedded pair for the SSPERK\((4,3)\)  method can be found in [1]} (Example 6.1.). The construction of this embedded pair \(\tilde{b}^T_1=\left[\frac{1}{3},\frac{1}{3},\frac{1}{3},0\right]\)  is related to the SSPERK\((3,2)\)  method. Taking into account the Butcher forms of the SSPERK\((s,2)\)  and SSPERK\((s,3)\)  methods, one can realize that this kind of embedded pair can be only achieved in this exceptional case. Taking into account the desired properties (i)-(iv) our numerical searches suggest the embedded pair
\(\tilde{b}^T_2=\left[\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{4}\right].\) 
